Without seeing some sample files it's impossible to say for sure whether this will be possible using a script, though.
Also, it can't actually rename the file, just save a copy of it under the new name.
saving a copy with a new name is fine. They are all like bank statement for example - the name of the account holder will be on the first page of every pdf.
If you can share some sample files please send them to me to [try6776 at gmail.com] and I'll let you know if I thin it's doable or not.
I wouldn't discount the Evermap plug-in. It's fast and efficient. Well worth the cost.
I've written many scripts for extracting data from PDFs, and it is not nearly as efficient.
And as try67 implies, the feasibility of reliably extracting the data depends on the difficulty of identifying it.